Analog-to-digital converters (ADCs) are often found in signal receiving applications such as radio receivers. In a radio receiver, a radio frequency (RF) analog signal is frequency down-converted by a mixer. The mixer uses a local oscillator (LO) signal from a local oscillator source to convert the received signal into a frequency range suitable for sampling by an analog-to-digital converter. Another oscillator controls the sampling rate of the analog-to-digital converter. A filter is required between the mixer and the analog-to-digital converter in order to minimize spurious signals caused by the mixing and the sampling processes.
The filter is sometimes referred to as “anti-aliasing” filter because it suppresses the spectral components that are outside the Nyquist band. In other words, it prevents out-of-band frequency components caused by the mixing and sampling, (i.e., the aliased signals), from contaminating the analog-to-digital converter output. Absent such a filter, part of the frequency spectrum outside the desired frequency band will be aliased into the desired frequency band producing undesired spurious signals. This aliasing effect may also occur even when such a filter is used, if it is not sufficiently accurately designed or manufactured.
An example of this aliasing effect is now described in conjunction with the frequency spectrums shown in FIGS. 1A-1G. FIG. 1A illustrates the location of the desired received signal frequency band, Aoo, and its negative counterpart aoo. FIG. 1B shows the frequency spectrum for the local oscillator (LO) signal used by the mixer to frequency down-convert the received RF signal into the intermediate frequency (IF) band, baseband, or other frequency band suitable for analog-to-digital conversion. The local oscillator signal has a fundamental frequency at ±L, a second harmonic at ±2L, a third harmonic at ±3L, a fourth harmonic at ±4L, a fifth harmonic at ±5L, and so on. Typically, only the odd harmonics are problematic because the even harmonics are generally very small in magnitude.
FIG. 1C illustrates the result of mixing of the local oscillator frequency fundamental frequency L (shown in FIG. 1B) and the receive band of the desired signal shown in FIG. 1A. The desired signal and its negative image have been shifted to lower frequency bands A0, a0 and to higher frequency bands A1, a1, (which are outside the frequency band of interest) with first order harmonics of FLO(±L). FIG. 1D illustrates the result of mixing the third order harmonic of the local oscillator signal (±3L) and the receive band, resulting in the spectrum components B0, b0 and A2, a2. Similarly, FIG. 1E shows the result of mixing the fifth order harmonics of the local oscillator signal (±5L) and the receive band, resulting in the spectrum components B1, b1. Again, only the odd-order harmonics of the local oscillator are of practical concern.
FIG. 1F shows the spectral result of the output of the mixer when the fundamental and the odd harmonics of the local oscillator are mixed with the desired signal in the receive band. A filter characteristic, represented as the thick-line trapezoid, can remove those unwanted spectral components shown in dotted lines, leaving only the desired signal at a0, A0 along with those undesired spectral components that were not filtered, e.g., b0, B0. Unfortunately, these in-band, third or higher order harmonics cause undesired aliasing in the analog-to-digital conversion.
FIG. 1G shows a sampled mixer output from an analog-to-digital converter, when a non-optimal filter, such as that shown in FIG. 1F, is used to filter the mixer output. The undesired, aliased signals are shown as “dotted” spectrums, and the desired signals are shown as “hatched” spectrums. The sampling frequency of the analog-to-digital converter and its harmonics are shown as thick black vertical lines centered for each spectral copy and are indicated as FADC. The aliasing problem is particularly troublesome when the analog-to-digital converter sampling rate is relatively high or higher than the local oscillator frequency. Although the sampling frequency satisfies the Nyquist sampling theorem and is more than twice the highest frequency of the receive band for the desired signal a0, A0, the sampling frequency is not more than twice the highest frequency of the mixer products b0, B0. As a result, those sampled, third harmonic signals b0, B0 are aliased into the frequency range of the desired signals. Being in the desired frequency band, the aliased signals cannot be readily removed by a filter, (e.g., a digital filter).
Thus, it is clear that the mixer output filter performs an important function in the receiver. However, such filters, (assuming they can perform the required filtering function), have their disadvantages. First, they must be very accurately designed and constructed in order to eliminate the aliasing effect. To do this, the filter must be usually of a high order so that it has a sharp cutoff and a low ripple in the pass band in order to remove all signals except a0, A0 in FIG. 1F. Second, such filters are typically expensive, and even then, have certain variances and losses in the pass band that require compensation. Third, the filter must be matched to both source and load impedance in order to function properly. The mixer “source” impedance is typically low, and the analog-to-digital converter “load” impedance is typically high and slightly capacitive. Because high performance analog-to-digital converters usually suffer from decreasing linearity as the voltage swing over their input increases, it is beneficial to keep the load impedance as low as possible. Impedance matching is difficult because of the non-linear input impedance of the analog-to-digital converter, which means there is no fixed impedance value to use as a reference when calculating the filter impedance level. This non-linear impedance results in an anti-aliasing filter whose transfer function depends on the input signal's amplitude and frequency. As a result, the filter's bandwidth, insertion loss, and ripple will not match specifications for a fixed load impedance. Thus, there are several reasons why it is undesirable to use a filter or impedance transformer between the mixer and the analog-to-digital converter. Still, there is a need to avoid spurious signals in the pass band caused by aliasing.
The present invention solves the above problems and meets certain desirable objectives by providing a method and apparatus that eliminates the need for such an anti-aliasing filter while, at the same time, ensuring that aliasing in the pass band does not occur as a result of the mixing and sampling processes. In particular, the present invention relates the mixer's local oscillator frequency with the frequency of the analog-to-digital converter sampling rate in such a way so as to avoid aliasing in the desired receive band. In particular, the frequency of the local oscillator signal is an integer multiple of half of a sampling rate of the analog-to-digital converter. When the integer is one, the frequency of the local oscillator signal is one half of the sampling rate of the analog-to-digital converter. In a preferred, non-limiting, example embodiment, the sampling rate of the analog-to-digital converter and the frequency of the local oscillator are related by the following: FLO=n*FADC/2, where n is any positive integer.
A common oscillator is preferably (though not necessarily) used to generate a periodic signal that is then used to generate both the local oscillator signal and the sampling rate signal. A frequency changer, receiving the periodic signal from the common oscillator, provides the local oscillator signal to the mixer and a sampling signal to the analog-to-digital converter. The frequency changer includes a first frequency divider for dividing the periodic signal in half to generate the local oscillator signal and for dividing the periodic signal by a positive integer to generate the sampling signal of the analog-to-digital converter.
The present invention may be used in a receiver without an anti-aliasing filter between the mixer and the analog-to-digital converter. Thus, the expense of such filter is avoided. In addition, the low impedance output of the mixer can be directly coupled to the analog-to-digital converter without an impedance matching network. Alternatively, a simplified, less expensive filter may used between the mixer and the analog-to-digital converter.